CN106684854A - Voltage off-limit risk analysis method of active power distribution network based on node equivalency - Google Patents

Abstract

The invention provides a voltage off-limit risk analysis method of an active power distribution network based on node equivalency. The method comprises the following steps that an equivalent state model of the active power distribution network is established; the voltage off-limit possibilities of different equivalent nodes in the discrete state are calculated; and the voltage off-limit possibility in the practical operation state of a node load is calculated. The characteristics that simplified nodes include fewer equivalent state parameters and an integrated influence of different operation states of the system on the node voltage can be represented are used, discrete states of the equivalent nodes in the active power distribution network can be selected according to node characteristics to carry out offline calculation and generate a corresponding database, and a reference calculation sample is provided for online rapid analysis; problems in rapidly and accurately calculating the node off-limit probabilities of the different nodes of the active power distribution network in practical operation are solved effectively; and the method is helpful for rapid online analysis and calculation, and has a higher accuracy.

Description

A kind of active power distribution network voltage limit risk analysis method based on node equivalent

Technical field

The present invention relates to a kind of analysis method, and in particular to a kind of active power distribution network voltage limit risk based on node equivalent is analyzed Method.

Background technology

With increasingly sharpening for the energy and environmental problem, new and renewable sources of energy generation technology obtains fast development, promotes Also obtain increasingly being widely applied using regenerative resource and for the centralized effectively supplementary distributed generation technology that generates electricity.Make For the important representative of distributed generation technology, in active power distribution network, photovoltaic generating system is with small scale, easily installing, dispersion spirit The superiority developments such as work, clean energy are projected the most.But with the continuous rising of photovoltaic system permeability, because it receives environment shadow Sound is larger, and power output has very strong randomness and fluctuation, and a series of power quality problems are brought to user.It is especially high Permeability photovoltaic system is likely to result in active power distribution network and overvoltage situation occurs so that voltage limit risk is more prominent and complicated.

For the active power distribution network containing load and the dual uncertain factor of photovoltaic generation, voltage limit risk analysis is carried out to it Calculating is converted into randomness computational problem by deterministic parameters calculation problem, replaces traditional certainty Load flow calculation complete by Probabilistic Load Flow Into the analytical calculation containing uncertainty models.This method has taken into full account the power probability model characteristics of load and photovoltaic system, Relative to the corresponding centrifugal pump of deterministic models particular point, configuration feature of the voltage in possible value can be more characterized.Ask The method of solution Probabilistic Load Flow mainly includes simulation, analytic method and approximation method.Wherein simulation is simulated each by substantial amounts of sampling Uncertain factor and combinations thereof is planted, theoretically it using accurate non-linear tidal current computing method, and be able to can consider not Determine the correlation between factor, therefore it is minimum to calculate the limitation of accuracy.But it is present, and amount of calculation is excessive, time-consuming Problem, constrains its application in actual motion.Analytic method needs to carry out substantial amounts of convolution fortune on the basis of approximate linearization Calculate.And approximation method can directly ask for the probability statistics feature of object function, but to the probability distribution outside Normal probability distribution There is certain error.

If consider each node load and multiple photovoltaic cells multidimensional ambiguous models in active power distribution network, and section cannot be ensured The Voltage Distribution of point voltage necessarily meets normal distribution.Therefore more accurate simulation is either adopted, or selects tool The analytic method and approximation method for having certain limitation all cannot be avoided the defect that amount of calculation is excessive or calculation error is larger.

The content of the invention

In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a kind of active power distribution network voltage out-of-limit wind based on node equivalent Dangerous analysis method, takes into full account the stochastic behaviour of load and distributed power source, carries out active power distribution network voltage out-of-limit probability analysis meter Calculate, electricity quality evaluation is carried out to active power distribution network in actual motion, and accordingly controlled according to analysis and assessment result.

In order to realize foregoing invention purpose, the present invention is adopted the following technical scheme that：

The present invention provides a kind of active power distribution network voltage limit risk analysis method based on node equivalent, and the analysis method includes Following steps：

Step 1：Node equivalent Load Probability model is set up, and with reference to photovoltaic system intensity of illumination stochastic model, sets up active matching somebody with somebody Electrical network equivalent state model；

Step 2：Probabilistic loadflow calculating is carried out to each equivalent node discrete state, and each equivalent section is calculated according to probabilistic loadflow result Voltage out-of-limit probability under point discrete state；

Step 3：The consecutive value of node load actual motion state lower node equivalent state parameter is searched in offline database, and Voltage out-of-limit probability under calculate node load actual motion state.

The step 1 is comprised the following steps：

Step 1-1：Each node peak load state in active power distribution network is chosen, node equivalent Load Probability model is set up；

Step 1-2：With reference to photovoltaic system intensity of illumination stochastic model, active power distribution network equivalent state model is set up.

In step 1-1, setting up node equivalent Load Probability model includes：

Assume that node h and node k is any two adjacent node, node h and node k forms circuit hk, has：

Wherein,The pressure drop vector between node h and node k is represented,Represent the current phasor of circuit hk, R_hkRepresent line The resistance of road hk, X_hkThe reactance of circuit hk is represented,Node k potential vectors are represented,The multiple work(of node k is flow through in expression Rate；

Ignore line loss, thenIt is expressed as：

Wherein, j=1,2 ..., N_k, N_kRepresent all nodes after the active power distribution network interior joint k that enters from terms of circuit hk head ends Set,Represent the load complex power of node j；

AssumeRepresent the rated voltage vector of active power distribution network, E_nRepresent the specified electricity of active power distribution network Pressure vector magnitude, thenIt is expressed as again：

Wherein,RepresentConjugation,Represent the impedance vector of circuit hk；

Therefore, for any equivalent node i in active power distribution network, have：

Wherein,Represent the pressure drop vector between equivalent node i and active power distribution network median generatrix, L_iRepresent equivalent node i and have All line sets between the power distribution network median generatrix of source,RepresentConjugation；

If only existing equivalent node i on-loads in active power distribution network,It is represented by again：

Wherein,The impedance sum between equivalent node i and active power distribution network median generatrix is represented,RepresentConjugation, Represent the complex power of equivalent node i；

Because load power has stochastic volatility, the then short-term fluctuation of each node load active power and reactive power short-term fluctuation Normal distribution is satisfied by, is then obtained by formula (5) and (6)：

And have：

Wherein, a_hkRepresentReal part, b_hkRepresentImaginary part；P_kRepresent all after active power distribution network interior joint k Node burden with power sum, i.e.,P_jRepresent the burden with power of node j；Q_kRepresent active power distribution network interior joint k All node load or burden without work sums afterwards, i.e.,Q_jRepresent the load or burden without work of node j；

Then can be obtained by the linear law of normal distribution：

Wherein, E (P_eqi) represent that the equivalent burden with power of equivalent node i is expected, E (Q_eqi) represent that equivalent node i's is equivalent idle Load expectation, P_eqiRepresent the equivalent burden with power of equivalent node i, Q_eqiRepresent the equivalent load or burden without work of equivalent node i, E (P_j) Represent the burden with power expectation of node j, E (Q_j) represent that the load or burden without work of node j is expected；

Because formula (10) is unsatisfactory for Independence for Random Variables, it is deformed into：

And have：

Wherein, N_nodeRepresent load bus set in active power distribution network, m=1,2 ..., N_node；RepresentConjugation,Table Show the complex power of load bus m；L_mRepresent load bus m place circuits and L_iIt is upper to there is the intersection point nearest away from load bus m When bus to all line sets between the intersection point；P_mRepresent the burden with power of load bus m, Q_mRepresent load bus m's Load or burden without work；c_mAnd d_mRepresent respectivelyReal part and imaginary part；

Then have：

Wherein, σ (P_eqi) represent equivalent node i equivalent burden with power standard deviation, σ (Q_eqi) represent equivalent node i equivalent nothing Workload standard deviation, D (P_eqi) represent equivalent node i equivalent burden with power variance, D (Q_eqi) represent that equivalent node i's is equivalent Load or burden without work variance, D (P_m) represent load bus m burden with power variance, D (Q_m) represent load bus m load or burden without work Variance.

In step 1-2, in photovoltaic system intensity of illumination stochastic model, Intensity of the sunlight obeys Beta distributions, sunshine Expect to represent that then active power distribution network equivalent state model is expressed as with E (S) according to intensity：

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

Wherein, σ (P_eqi) represent equivalent node i equivalent burden with power standard deviation, σ (Q_eqi) represent equivalent node i equivalent nothing Workload standard deviation, E (P_eqi) represent that the equivalent burden with power of equivalent node i is expected, E (Q_eqi) represent that equivalent node i's is equivalent Load or burden without work is expected.

The step 2 is comprised the following steps：

Step 2-1：Choose each equivalent node discrete state in active power distribution network；

Step 2-2：Probabilistic loadflow calculating is carried out to each equivalent node discrete state using Latin Hypercube Sampling, probabilistic loadflow is obtained As a result；

Step 2-3：According to probabilistic loadflow result, and voltage out-of-limit probability under each equivalent node discrete state is calculated using law of great number；

Step 2-4：Voltage out-of-limit probability under each equivalent node discrete state is preserved to offline database.

The step 3 is comprised the following steps：

Step 3-1：Obtain each node load actual motion state and photovoltaic system actual motion state；

Step 3-2：The consecutive value of node load actual motion state lower node equivalent state parameter is searched in offline database；

Step 3-3：Using the voltage out-of-limit probability under multidimensional Lagrange interpolation calculation node load actual motion state, and Voltage limit risk is analyzed.

In step 3-2, node equivalent state parameter includes that Intensity of the sunlight expects that E (S), the equivalent of equivalent node i have Workload expects E (P_eqi), the equivalent burden with power standard deviation sigma (P of equivalent node i_eqi), the equivalent load or burden without work of equivalent node i Expect E (Q_eqi) and equivalent node i equivalent load or burden without work standard deviation sigma (Q_eqi)。

Step 3-3 is comprised the following steps：

Step 3-3-1：Using voltage out-of-limit probability under multidimensional Lagrange interpolation calculation node load actual motion state, bag Include：

Assume E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) the descending consecutive number that finds in offline database is respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi), the up consecutive number found in offline database is respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi), then the corresponding voltage out-of-limit probability f of consecutive number is obtained, have：

Wherein, j₁,j₂,...,j₅E (S), E (P are represented respectively_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) state index, value 0 or 1 is, i.e.,：

j₁,j₂,...,j₅When taking 0,Represent respectively E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) descending consecutive number；

j₁,j₂,...,j₅When taking 1,Represent respectively E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) up consecutive number；

WithRepresent the jth of E (S)₁Individual Interpolation-Radix-Function, i.e. j₁When taking 0,Represent the of E (S) 0 Interpolation-Radix-Function l₀(E(S))；j₁When taking 1,Represent the 1st Interpolation-Radix-Function l of E (S)₁(E(S))； l₀(E (S)) and l₁(E (S)) is expressed as：

WithRepresent E (P_eqi) jth₂Individual Interpolation-Radix-Function, i.e. j₂When taking 0,Represent E (P_eqi) 0th Interpolation-Radix-Function l₀(E(P_eqi))；j₂When taking 1,Represent E (P_eqi) the 1st Interpolation-Radix-Function l₁(E(P_eqi))；l₀(E(P_eqi)) and l₁(E(P_eqi)) be expressed as：

WithRepresent σ (P_eqi) jth₃Individual Interpolation-Radix-Function, i.e. j₃When taking 0,Represent σ (P_eqi) 0th Interpolation-Radix-Function l₀(σ(P_eqi))；j₃When taking 1,Represent σ (P_eqi) the 1st Interpolation-Radix-Function l₁(σ(P_eqi))；l₀(σ(P_eqi)) and l₁(σ(P_eqi)) be expressed as：

WithRepresent E (Q_eqi) jth₄Individual Interpolation-Radix-Function, i.e. j₄When taking 0,Represent E(Q_eqi) the 0th Interpolation-Radix-Function l₀(E(Q_eqi))；j₄When taking 1,Represent E (Q_eqi) the 1st Interpolation-Radix-Function l₁(E(Q_eqi))；l₀(E(Q_eqi)) and l₁(E(Q_eqi)) be expressed as：

WithRepresent σ (Q_eqi) jth₅Individual Interpolation-Radix-Function, i.e. j₅When taking 0,Represent σ(Q_eqi) the 0th Interpolation-Radix-Function l₀(σ(Q_eqi))；j₅When taking 1,Represent σ (Q_eqi) the 1st Interpolation-Radix-Function l₁(σ(Q_eqi))；l₀(σ(Q_eqi)) and l₁(σ(Q_eqi)) be expressed as：

Then, the voltage out-of-limit probability under node load actual motion state is obtained, is had：

Wherein, f (E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) represent that the voltage under node load actual motion state is got over Limit probability；

Step 3-3-2：According to f (E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) voltage limit risk is analyzed, have Body has：f(E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) bigger, voltage limit risk is bigger.

Compared with immediate prior art, the technical scheme that the present invention is provided has the advantages that：

1) present invention simplifies the active power distribution network running status for considering load and photovoltaic system stochastic behaviour using node equivalent method Parameter, impact of the whole system load comprehensive function to the node voltage is characterized using the equivalent load probabilistic model of individual node；

2) present invention is using each node equivalent state parameter negligible amounts after simplifying and can characterize the various running statuses of system to this The characteristics of node voltage combined influence effect, proposition can choose each equivalent node discrete state in active power distribution network according to nodal properties Carry out off-line calculation and generate associated databases, provide with reference to calculating sample for online quick analysis；

3) present invention proposition is calculated using node equivalent principle and answers this each node random parameter, i.e., in power distribution network actual motion Consecutive value can be searched in offline database, multigroup discrete state is formed and is obtained so as to carry out quick multiple dimension Lagrange interpolation calculations The out-of-limit probability of node voltage, and using all kinds of probabilistic loadflow methods and while consider the direct solving method ratio of multiple stochastic variables Compared with, this method is more beneficial for fast on-line analyzing calculating, and with high accuracy；

4) effectively solving of the present invention fast and accurately calculates asking for the active power distribution network out-of-limit probability of each node voltage in actual motion Topic.

Description of the drawings

Fig. 1 is to calculate voltage out-of-limit probability flow chart under each equivalent node discrete state using law of great number in the embodiment of the present invention；

Fig. 2 is using voltage out-of-limit under multidimensional Lagrange interpolation calculation node load actual motion state in the embodiment of the present invention Probability flow chart.

Specific embodiment

The present invention is described in further detail below in conjunction with the accompanying drawings.

The present invention provides a kind of active power distribution network voltage limit risk analysis method based on node equivalent, using off-line calculation and The method that line analysis combines, solves the problems, such as fast and accurately to calculate the out-of-limit probability of each node voltage of power distribution network in actual motion.

(1) the distribution system running state parameter for considering load and distributed power source stochastic behaviour is simplified so as to be conducive to offline meter During calculation when the selection and on-line analysis of typicalness actual motion state mapping；

(2) according to the distribution system running state parameter after simplification, by being chosen to typical discrete state and based on simulation Load flow calculation immediately, form offline typicalness and voltage out-of-limit probability analysis result database, it is fast when being on-line operation Speed is calculated and laid the foundation；

(3) actual motion characteristic is equivalent to by the operational factor after simplifying according to node equivalent principle, and is looked in offline database Each equivalent operational factor consecutive value is looked for, voltage out-of-limit probability during actual motion is quickly calculated eventually through the mode of multi-dimensional interpolation.

The present invention provides a kind of active power distribution network voltage limit risk analysis method based on node equivalent, and the analysis method includes Following steps：

Step 1：Node equivalent Load Probability model is set up, and with reference to photovoltaic system intensity of illumination stochastic model, sets up active matching somebody with somebody Electrical network equivalent state model；

Step 2：Probabilistic loadflow calculating is carried out to each equivalent node discrete state, and each equivalent section is calculated according to probabilistic loadflow result Voltage out-of-limit probability under point discrete state；

Step 3：The consecutive value of node load actual motion state lower node equivalent state parameter is searched in offline database, and Voltage out-of-limit probability under calculate node load actual motion state.

The step 1 is comprised the following steps：

Step 1-1：Each node peak load state in active power distribution network is chosen, node equivalent Load Probability model is set up；

Step 1-2：With reference to photovoltaic system intensity of illumination stochastic model, active power distribution network equivalent state model is set up.

In step 1-1, setting up node equivalent Load Probability model includes：

Assume that node h and node k is any two adjacent node, node h and node k forms circuit hk, has：

Wherein,The pressure drop vector between node h and node k is represented,Represent the current phasor of circuit hk, R_hkRepresent line The resistance of road hk, X_hkThe reactance of circuit hk is represented,Node k potential vectors are represented,The multiple work(of node k is flow through in expression Rate；

Ignore line loss, thenIt is expressed as：

Wherein, j=1,2 ..., N_k, N_kRepresent all nodes after the active power distribution network interior joint k that enters from terms of circuit hk head ends Set,Represent the load complex power of node j；

AssumeRepresent the rated voltage vector of active power distribution network, E_nRepresent the specified electricity of active power distribution network Pressure vector magnitude, thenIt is expressed as again：

Wherein,RepresentConjugation,Represent the impedance vector of circuit hk；

Therefore, for any equivalent node i in active power distribution network, have：

Wherein,Represent the pressure drop vector between equivalent node i and active power distribution network median generatrix, L_iRepresent equivalent node i and have All line sets between the power distribution network median generatrix of source,RepresentConjugation；

If only existing equivalent node i on-loads in active power distribution network,It is represented by again：

Wherein,The impedance sum between equivalent node i and active power distribution network median generatrix is represented,RepresentConjugation, Represent the complex power of equivalent node i；

Because load power has stochastic volatility, the then short-term fluctuation of each node load active power and reactive power short-term fluctuation Normal distribution is satisfied by, is then obtained by formula (5) and (6)：

And have：

Wherein, a_hkRepresentReal part, b_hkRepresentImaginary part；P_kRepresent all after active power distribution network interior joint k Node burden with power sum, i.e.,P_jRepresent the burden with power of node j；Q_kRepresent active power distribution network interior joint k All node load or burden without work sums afterwards, i.e.,Q_jRepresent the load or burden without work of node j；

Then can be obtained by the linear law of normal distribution：

Wherein, E (P_eqi) represent that the equivalent burden with power of equivalent node i is expected, E (Q_eqi) represent that equivalent node i's is equivalent idle Load expectation, P_eqiRepresent the equivalent burden with power of equivalent node i, Q_eqiRepresent the equivalent load or burden without work of equivalent node i, E (P_j) Represent the burden with power expectation of node j, E (Q_j) represent that the load or burden without work of node j is expected；

Because formula (10) is unsatisfactory for Independence for Random Variables, it is deformed into：

And have：

Wherein, N_nodeRepresent load bus set in active power distribution network, m=1,2 ..., N_node；RepresentConjugation,Table Show the complex power of load bus m；L_mRepresent load bus m place circuits and L_iIt is upper to there is the intersection point nearest away from load bus m When bus to all line sets between the intersection point；P_mRepresent the burden with power of load bus m, Q_mRepresent load bus m's Load or burden without work；c_mAnd d_mRepresent respectivelyReal part and imaginary part；

Then have：

Wherein, σ (P_eqi) represent equivalent node i equivalent burden with power standard deviation, σ (Q_eqi) represent equivalent node i equivalent nothing Workload standard deviation, D (P_eqi) represent equivalent node i equivalent burden with power variance, D (Q_eqi) represent that equivalent node i's is equivalent Load or burden without work variance, D (P_m) represent load bus m burden with power variance, D (Q_m) represent load bus m load or burden without work Variance.

In step 1-2, in photovoltaic system intensity of illumination stochastic model, Intensity of the sunlight obeys Beta distributions, sunshine Expect to represent that then active power distribution network equivalent state model is expressed as with E (S) according to intensity：

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

Wherein, σ (P_eqi) represent equivalent node i equivalent burden with power standard deviation, σ (Q_eqi) represent equivalent node i equivalent nothing Workload standard deviation, E (P_eqi) represent that the equivalent burden with power of equivalent node i is expected, E (Q_eqi) represent that equivalent node i's is equivalent Load or burden without work is expected.

Such as Fig. 1, the step 2 is comprised the following steps：

Step 2-1：Choose each equivalent node discrete state in active power distribution network；

Step 2-2：Probabilistic loadflow calculating is carried out to each equivalent node discrete state using Latin Hypercube Sampling, probabilistic loadflow is obtained As a result；

Step 2-3：According to probabilistic loadflow result, and voltage out-of-limit probability under each equivalent node discrete state is calculated using law of great number；

Step 2-4：Voltage out-of-limit probability under each equivalent node discrete state is preserved to offline database.

Such as Fig. 2, the step 3 is comprised the following steps：

Step 3-1：Obtain each node load actual motion state and photovoltaic system actual motion state；

Step 3-2：The consecutive value of node load actual motion state lower node equivalent state parameter is searched in offline database；

Step 3-3：Using the voltage out-of-limit probability under multidimensional Lagrange interpolation calculation node load actual motion state, and Voltage limit risk is analyzed.

In step 3-2, node equivalent state parameter includes that Intensity of the sunlight expects that E (S), the equivalent of equivalent node i have Workload expects E (P_eqi), the equivalent burden with power standard deviation sigma (P of equivalent node i_eqi), the equivalent load or burden without work of equivalent node i Expect E (Q_eqi) and equivalent node i equivalent load or burden without work standard deviation sigma (Q_eqi)。

Step 3-3 is comprised the following steps：

Step 3-3-1：Using voltage out-of-limit probability under multidimensional Lagrange interpolation calculation node load actual motion state, bag Include：

Assume E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) the descending consecutive number that finds in offline database is respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi), the up consecutive number found in offline database is respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi), then the corresponding voltage out-of-limit probability f of consecutive number is obtained, have：

Wherein, j₁,j₂,...,j₅E (S), E (P are represented respectively_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) state index, value 0 or 1 is, i.e.,：

j₁,j₂,...,j₅When taking 0,Represent respectively E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) descending consecutive number；

j₁,j₂,...,j₅When taking 1,Represent respectively E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) up consecutive number；

WithRepresent the jth of E (S)₁Individual Interpolation-Radix-Function, i.e. j₁When taking 0,Represent the of E (S) 0 Interpolation-Radix-Function l₀(E(S))；j₁When taking 1,Represent the 1st Interpolation-Radix-Function l of E (S)₁(E(S))； l₀(E (S)) and l₁(E (S)) is expressed as：

WithRepresent E (P_eqi) jth₂Individual Interpolation-Radix-Function, i.e. j₂When taking 0,Represent E (P_eqi) 0th Interpolation-Radix-Function l₀(E(P_eqi))；j₂When taking 1,Represent E (P_eqi) the 1st Interpolation-Radix-Function l₁(E(P_eqi))；l₀(E(P_eqi)) and l₁(E(P_eqi)) be expressed as：

WithRepresent σ (P_eqi) jth₃Individual Interpolation-Radix-Function, i.e. j₃When taking 0,Represent σ (P_eqi) 0th Interpolation-Radix-Function l₀(σ(P_eqi))；j₃When taking 1,Represent σ (P_eqi) the 1st Interpolation-Radix-Function l₁(σ(P_eqi))；l₀(σ(P_eqi)) and l₁(σ(P_eqi)) be expressed as：

WithRepresent E (Q_eqi) jth₄Individual Interpolation-Radix-Function, i.e. j₄When taking 0,Represent E(Q_eqi) the 0th Interpolation-Radix-Function l₀(E(Q_eqi))；j₄When taking 1,Represent E (Q_eqi) the 1st Interpolation-Radix-Function l₁(E(Q_eqi))；l₀(E(Q_eqi)) and l₁(E(Q_eqi)) be expressed as：

WithRepresent σ (Q_eqi) jth₅Individual Interpolation-Radix-Function, i.e. j₅When taking 0,Represent σ(Q_eqi) the 0th Interpolation-Radix-Function l₀(σ(Q_eqi))；j₅When taking 1,Represent σ (Q_eqi) the 1st Interpolation-Radix-Function l₁(σ(Q_eqi))；l₀(σ(Q_eqi)) and l₁(σ(Q_eqi)) be expressed as：

Then, the voltage out-of-limit probability under node load actual motion state is obtained, is had：

Wherein, f (E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) represent that the voltage under node load actual motion state is got over Limit probability；

Step 3-3-2：According to f (E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) voltage limit risk is analyzed, have Body has：f(E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) bigger, voltage limit risk is bigger.

Finally it should be noted that：Above example only to illustrate technical scheme rather than a limitation, art Those of ordinary skill with reference to above-described embodiment still can to the present invention specific embodiment modify or equivalent, These any modifications or equivalent without departing from spirit and scope of the invention, are applying for pending claim of the invention Within protection domain.

Claims (8)

1. a kind of active power distribution network voltage limit risk analysis method based on node equivalent, it is characterised in that：The analysis method Comprise the following steps：

Step 1：Node equivalent Load Probability model is set up, and with reference to photovoltaic system intensity of illumination stochastic model, sets up active matching somebody with somebody Electrical network equivalent state model；

Step 2：Probabilistic loadflow calculating is carried out to each equivalent node discrete state, and each equivalent section is calculated according to probabilistic loadflow result Voltage out-of-limit probability under point discrete state；

Step 3：The consecutive value of node load actual motion state lower node equivalent state parameter is searched in offline database, and Voltage out-of-limit probability under calculate node load actual motion state.

2. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 1, its feature exists In：The step 1 is comprised the following steps：

Step 1-1：Each node peak load state in active power distribution network is chosen, node equivalent Load Probability model is set up；

Step 1-2：With reference to photovoltaic system intensity of illumination stochastic model, active power distribution network equivalent state model is set up.

3. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 2, its feature exists In：In step 1-1, setting up node equivalent Load Probability model includes：

Assume that node h and node k is any two adjacent node, node h and node k forms circuit hk, has：

${\stackrel{\·}{V}}_{hk}={\stackrel{\·}{I}}_{hk}(R_{hk}+{\mathrm{jX}}_{hk})={\left(\frac{{\stackrel{\‾}{S}}_k}{{\stackrel{\·}{E}}_k}\right)}^{*}(R_{hk}+{\mathrm{jX}}_{hk})---\left(1\right)$

Wherein,The pressure drop vector between node h and node k is represented,Represent the current phasor of circuit hk, R_hkRepresent line The resistance of road hk, X_hkThe reactance of circuit hk is represented,Node k potential vectors are represented,The multiple work(of node k is flow through in expression Rate；

Ignore line loss, thenIt is expressed as：

${\stackrel{\‾}{S}}_k=\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j---\left(2\right)$

Wherein, j=1,2 ..., N_k, N_kRepresent all nodes after the active power distribution network interior joint k that enters from terms of circuit hk head ends Set,Represent the load complex power of node j；

Assume Represent the rated voltage vector of active power distribution network, E_nRepresent the specified electricity of active power distribution network Pressure vector magnitude, thenIt is expressed as again：

${\stackrel{\·}{V}}_{hk}=\frac{1}{E_n}{\stackrel{\‾}{S}}_k^{*}{\stackrel{\·}{Z}}_{hk}=\frac{{\stackrel{\‾}{S}}_k^{*}}{E_n}(R_{hk}+{\mathrm{jX}}_{hk})---\left(3\right)$

Wherein,RepresentConjugation,Represent the impedance vector of circuit hk；

Therefore, for any equivalent node i in active power distribution network, have：

${\stackrel{\·}{V}}_{0i}=\underset{hk\∈L_i}{\Σ}{\stackrel{\·}{V}}_{hk}=\underset{hk\∈L_i}{\Σ}\[\frac{{\stackrel{\·}{Z}}_{hk}}{E_n}\left(\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j^{*}\right)\]---\left(4\right)$

Wherein,Represent the pressure drop vector between equivalent node i and active power distribution network median generatrix, L_iRepresent equivalent node i and have All line sets between the power distribution network median generatrix of source,RepresentConjugation；

If only existing equivalent node i on-loads in active power distribution network,It is represented by again：

${\stackrel{\·}{V}}_{0i}=\frac{{\stackrel{\·}{Z}}_{0i}{\stackrel{\‾}{S}}_{eqi}^{*}}{E_n}---\left(5\right)$

Wherein,The impedance sum between equivalent node i and active power distribution network median generatrix is represented,RepresentConjugation, Represent the complex power of equivalent node i；

Because load power has stochastic volatility, the then short-term fluctuation of each node load active power and reactive power short-term fluctuation Normal distribution is satisfied by, is then obtained by formula (5) and (6)：

${\stackrel{\‾}{S}}_{eqi}^{*}=\underset{hk\∈L_i}{\Σ}\[\frac{{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}\left(\underset{j\∈N_k}{\Σ}{\stackrel{\‾}{S}}_j^{*}\right)\]=\underset{hk\∈L_i}{\Σ}\[(a_{hk}{P}_k+b_{hk}{Q}_k)+j(b_{hk}{P}_k-a_{hk}{Q}_k)\]---\left(6\right)$

And have：

$\frac{{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}=a_{hk}+{\mathrm{jb}}_{hk}---\left(7\right)$

Wherein, a_hkRepresentReal part, b_hkRepresentImaginary part；P_kRepresent all after active power distribution network interior joint k Node burden with power sum, i.e.,P_jRepresent the burden with power of node j；Q_kRepresent active power distribution network interior joint k All node load or burden without work sums afterwards, i.e.,Q_jRepresent the load or burden without work of node j；

Then can be obtained by the linear law of normal distribution：

$E\left(P_{eqi}\right)=\underset{hk\∈L_i}{\Σ}\[a_{hk}\underset{j\∈N_k}{\Σ}E\left(P_j\right)+b_{hk}\underset{j\∈N_k}{\Σ}E\left(Q_j\right)\]---\left(8\right)$

$E\left(Q_{eqi}\right)=\underset{hk\∈L_i}{\Σ}\[a_{hk}\underset{j\∈N_k}{\Σ}E\left(Q_j\right)-b_{hk}\underset{j\∈N_k}{\Σ}E\left(P_j\right)\]---\left(9\right)$

Wherein, E (P_eqi) represent that the equivalent burden with power of equivalent node i is expected, E (Q_eqi) represent that equivalent node i's is equivalent idle Load expectation, P_eqiRepresent the equivalent burden with power of equivalent node i, Q_eqiRepresent the equivalent load or burden without work of equivalent node i, E (P_j) Represent the burden with power expectation of node j, E (Q_j) represent that the load or burden without work of node j is expected；

Because formula (10) is unsatisfactory for Independence for Random Variables, it is deformed into：

${\stackrel{\‾}{S}}_{eqi}^{*}=\frac{\underset{m\∈N_{node}}{\Σ}\[{\stackrel{\‾}{S}}_m^{*}\underset{hk\∈L_m}{\Σ}{\stackrel{\·}{Z}}_{hk}\]}{{\stackrel{\·}{Z}}_{0i}}=\underset{m\∈N_{node}}{\Σ}\[\left(c_m{P}_m+d_m{Q}_m\right)+j\left(d_m{P}_m-c_m{Q}_m\right)\]---\left(10\right)$

And have：

$\frac{\underset{hk\∈L_m}{\Σ}{\stackrel{\·}{Z}}_{hk}}{{\stackrel{\·}{Z}}_{0i}}=c_m+{\mathrm{jd}}_m---\left(11\right)$

Wherein, N_nodeRepresent load bus set in active power distribution network, m=1,2 ..., N_node；RepresentConjugation,Table Show the complex power of load bus m；L_mRepresent load bus m place circuits and L_iIt is upper to there is the intersection point nearest away from load bus m When bus to all line sets between the intersection point；P_mRepresent the burden with power of load bus m, Q_mRepresent load bus m's Load or burden without work；c_mAnd d_mRepresent respectivelyReal part and imaginary part；

Then have：

$\mathrm{\σ}\left(P_{eqi}\right)=\sqrt{D\left(P_{eqi}\right)}=\sqrt{\underset{m\∈N_{node}}{\Σ}\[c_m^{2}D\left(P_m\right)+d_m^{2}D\left(Q_m\right)\]}---\left(12\right)$

$\mathrm{\σ}\left(Q_{eqi}\right)=\sqrt{D\left(Q_{eqi}\right)}=\sqrt{\underset{m\∈N_{node}}{\Σ}\[d_m^{2}D\left(P_m\right)+c_m^{2}D\left(Q_m\right)\]}---\left(13\right)$

Wherein, σ (P_eqi) represent equivalent node i equivalent burden with power standard deviation, σ (Q_eqi) represent equivalent node i equivalent nothing Workload standard deviation, D (P_eqi) represent equivalent node i equivalent burden with power variance, D (Q_eqi) represent that equivalent node i's is equivalent Load or burden without work variance, D (P_m) represent load bus m burden with power variance, D (Q_m) represent load bus m load or burden without work Variance.

4. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 3, its feature exists In：In step 1-2, in photovoltaic system intensity of illumination stochastic model, Intensity of the sunlight obeys Beta distributions, sunshine Expect to represent that then active power distribution network equivalent state model is expressed as with E (S) according to intensity：

{E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)} (14)

Wherein, σ (P_eqi) represent equivalent node i equivalent burden with power standard deviation, σ (Q_eqi) represent equivalent node i equivalent nothing Workload standard deviation, E (P_eqi) represent that the equivalent burden with power of equivalent node i is expected, E (Q_eqi) represent that equivalent node i's is equivalent Load or burden without work is expected.

5. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 1, its feature exists In：The step 2 is comprised the following steps：

Step 2-1：Choose each equivalent node discrete state in active power distribution network；

Step 2-2：Probabilistic loadflow calculating is carried out to each equivalent node discrete state using Latin Hypercube Sampling, probabilistic loadflow is obtained As a result；

Step 2-3：According to probabilistic loadflow result, and voltage out-of-limit probability under each equivalent node discrete state is calculated using law of great number；

Step 2-4：Voltage out-of-limit probability under each equivalent node discrete state is preserved to offline database.

6. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 1, its feature exists In：The step 3 is comprised the following steps：

Step 3-1：Obtain each node load actual motion state and photovoltaic system actual motion state；

Step 3-2：The consecutive value of node load actual motion state lower node equivalent state parameter is searched in offline database；

Step 3-3：Using the voltage out-of-limit probability under multidimensional Lagrange interpolation calculation node load actual motion state, and Voltage limit risk is analyzed.

7. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 6, its feature exists In：In step 3-2, node equivalent state parameter includes that Intensity of the sunlight expects that E (S), the equivalent of equivalent node i have Workload expects E (P_eqi), the equivalent burden with power standard deviation sigma (P of equivalent node i_eqi), the equivalent load or burden without work of equivalent node i Expect E (Q_eqi) and equivalent node i equivalent load or burden without work standard deviation sigma (Q_eqi)。

8. the active power distribution network voltage limit risk analysis method based on node equivalent according to claim 7, its feature exists In：Step 3-3 is comprised the following steps：

Step 3-3-1：Using voltage out-of-limit probability under multidimensional Lagrange interpolation calculation node load actual motion state, bag Include：

Assume E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) the descending consecutive number that finds in offline database is respectively E⁰(S),E⁰(P_eqi),σ⁰(P_eqi),E⁰(Q_eqi),σ⁰(Q_eqi), the up consecutive number found in offline database is respectively E¹(S),E¹(P_eqi),σ¹(P_eqi),E¹(Q_eqi),σ¹(Q_eqi), then the corresponding voltage out-of-limit probability f of consecutive number is obtained, have：

$f=f\left(E^{j_1}\right(S),E^{j_2}(P_{eqi}),{\mathrm{\σ}}^{j_3}(P_{eqi}),E^{j_4}(Q_{eqi}),{\mathrm{\σ}}^{j_5}(Q_{eqi}\left)\right)---\left(15\right)$

Wherein, j₁,j₂,...,j₅E (S), E (P are represented respectively_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) state index, value 0 or 1 is, i.e.,：

j₁,j₂,...,j₅When taking 0,Represent respectively E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) descending consecutive number；

j₁,j₂,...,j₅When taking 1,Represent respectively E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi) up consecutive number；

WithRepresent the jth of E (S)₁Individual Interpolation-Radix-Function, i.e. j₁When taking 0,Represent the of E (S) 0 Interpolation-Radix-Function l₀(E(S))；j₁When taking 1,Represent the 1st Interpolation-Radix-Function l of E (S)₁(E(S))； l₀(E (S)) and l₁(E (S)) is expressed as：

$l_0\left(E\right(S\left)\right)=\frac{E\left(S\right)-E^1\left(S\right)}{E^0\left(S\right)-E^1\left(S\right)}---\left(16\right)$

$l_1\left(E\right(S\left)\right)=\frac{E\left(S\right)-E^0\left(S\right)}{E^1\left(S\right)-E^0\left(S\right)}---\left(17\right)$

WithRepresent E (P_eqi) jth₂Individual Interpolation-Radix-Function, i.e. j₂When taking 0,Represent E (P_eqi) 0th Interpolation-Radix-Function l₀(E(P_eqi))；j₂When taking 1,Represent E (P_eqi) the 1st Interpolation-Radix-Function l₁(E(P_eqi))；l₀(E(P_eqi)) and l₁(E(P_eqi)) be expressed as：

$l_0\left(E\right(P_{eqi}\left)\right)=\frac{E\left(P_{eqi}\right)-E^1\left(P_{eqi}\right)}{E^0\left(P_{eqi}\right)-E^1\left(P_{eqi}\right)}---\left(18\right)$

$l_1\left(E\right(P_{eqi}\left)\right)=\frac{E\left(P_{eqi}\right)-E^0\left(P_{eqi}\right)}{E^1\left(P_{eqi}\right)-E^0\left(P_{eqi}\right)}---\left(19\right)$

WithRepresent σ (P_eqi) jth₃Individual Interpolation-Radix-Function, i.e. j₃When taking 0,Represent σ (P_eqi) 0th Interpolation-Radix-Function l₀(σ(P_eqi))；j₃When taking 1,Represent σ (P_eqi) the 1st Interpolation-Radix-Function l₁(σ(P_eqi))；l₀(σ(P_eqi)) and l₁(σ(P_eqi)) be expressed as：

$l_0\left(\mathrm{\σ}\right(P_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(P_{eqi}\right)-{\mathrm{\σ}}^1\left(P_{eqi}\right)}{{\mathrm{\σ}}^0\left(P_{eqi}\right)-{\mathrm{\σ}}^1\left(P_{eqi}\right)}---\left(20\right)$

$l_1\left(\mathrm{\σ}\right(P_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(P_{eqi}\right)-{\mathrm{\σ}}^0\left(P_{eqi}\right)}{{\mathrm{\σ}}^1\left(P_{eqi}\right)-{\mathrm{\σ}}^0\left(P_{eqi}\right)}---\left(21\right)$

WithRepresent E (Q_eqi) jth₄Individual Interpolation-Radix-Function, i.e. j₄When taking 0,Represent E(Q_eqi) the 0th Interpolation-Radix-Function l₀(E(Q_eqi))；j₄When taking 1,Represent E (Q_eqi) the 1st Interpolation-Radix-Function l₁(E(Q_eqi))；l₀(E(Q_eqi)) and l₁(E(Q_eqi)) be expressed as：

$l_0\left(E\right(Q_{eqi}\left)\right)=\frac{E\left(Q_{eqi}\right)-E^1\left(Q_{eqi}\right)}{E^0\left(Q_{eqi}\right)-E^1\left(Q_{eqi}\right)}---\left(22\right)$

$l_1\left(E\right(Q_{eqi}\left)\right)=\frac{E\left(Q_{eqi}\right)-E^0\left(Q_{eqi}\right)}{E^1\left(Q_{eqi}\right)-E^0\left(Q_{eqi}\right)}---\left(23\right)$

WithRepresent σ (Q_eqi) jth₅Individual Interpolation-Radix-Function, i.e. j₅When taking 0,Represent σ(Q_eqi) the 0th Interpolation-Radix-Function l₀(σ(Q_eqi))；j₅When taking 1,Represent σ (Q_eqi) the 1st Interpolation-Radix-Function l₁(σ(Q_eqi))；l₀(σ(Q_eqi)) and l₁(σ(Q_eqi)) be expressed as：

$l_0\left(\mathrm{\σ}\right(Q_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(Q_{eqi}\right)-{\mathrm{\σ}}^1\left(Q_{eqi}\right)}{{\mathrm{\σ}}^0\left(Q_{eqi}\right)-{\mathrm{\σ}}^1\left(Q_{eqi}\right)}---\left(24\right)$

$l_1\left(\mathrm{\σ}\right(Q_{eqi}\left)\right)=\frac{\mathrm{\σ}\left(Q_{eqi}\right)-{\mathrm{\σ}}^0\left(Q_{eqi}\right)}{{\mathrm{\σ}}^1\left(Q_{eqi}\right)-{\mathrm{\σ}}^0\left(Q_{eqi}\right)}---\left(25\right)$

Then, the voltage out-of-limit probability under node load actual motion state is obtained, is had：

$\begin{array}{c}f\left(E\left(S\right),E\left(P_{eqi}\right),\mathrm{\σ}\left(P_{eqi}\right),E\left(Q_{eqi}\right),\mathrm{\σ}\left(Q_{eqi}\right)\right)=\\ \underset{j_1=0}{\overset{1}{\Σ}}\underset{j_2=0}{\overset{1}{\Σ}}...\underset{j_5=0}{\overset{1}{\Σ}}\left[\begin{array}{c}{l}_{j_1}\left(E\left(S\right)\right)\×l_{j_2}\left(E\left(P_{eqi}\right)\right)\×l_{j_3}\left(\mathrm{\σ}\left(P_{eqi}\right)\right)\×l_{j_4}\left(E\left(Q_{eqi}\right)\right)\×l_{j_5}\left(\mathrm{\σ}\left(Q_{eqi}\right)\right)\\ \×f\left(E^{j_1}\left(S\right),E^{j_2}\left(P_{eqi}\right),{\mathrm{\σ}}^{j_3}\left(P_{eqi}\right),E^{j_4}\left(Q_{eqi}\right),{\mathrm{\σ}}^{j_5}\left(Q_{eqi}\right)\right)\end{array}\right]\end{array}---\left(26\right)$

Wherein, f (E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) represent that the voltage under node load actual motion state is got over Limit probability；

Step 3-3-2：According to f (E (S), E (P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) voltage limit risk is analyzed, have Body has：f(E(S),E(P_eqi),σ(P_eqi),E(Q_eqi),σ(Q_eqi)) bigger, voltage limit risk is bigger.